Many fish have specialized organs called buoyancy bladders which allow them to control their buoyancy - effectively rising or sinking in the water.

What if humans adapted this to use in the air? I'm picturing something like a balloon, strapped to the user's back, that filters specific gasses less dense or more dense than air to fill itself. It would be able to calculate what ratio of x to y was necessary to move the person up, down, etc.

$\begingroup$This is actually almost 100% exactly how hot air balloons work. Hot air (read: less dense) is pumped into the balloon when you wish to rise, and hot air is released out the top, thus pulling in cooler air (read: more dense) whenever you wish to fall.$\endgroup$
– MozerShmozerNov 11 '16 at 19:28

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$\begingroup$Well, technically Sky Lanterns fly this way, but they are by no means large enough to lift a person. In order to lift a human, you need a fairly large hot air balloon. Even if the lifting gas has near-zero density you would still need > 54 Litres of it to lift a 70 kg person, about the size of this backpack. The real issue here is that the air is so sparse on Earth, and therefore does not provide much buoyant lift.$\endgroup$
– MozerShmozerNov 11 '16 at 23:30

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$\begingroup$@EveryBitHelps It's the air on the outside that needs to be denser. The force actually at work to create buoyancy is gravity. Heavier gasses are pulled down with more force, and in order to make room for themselves they will squeeze lighter objects upward and out of the way. By filling a balloon with a low density gas, the average density of the gas + balloon is low enough that the heavier air around it can push the balloon upward. Increasing the density of the outside air (or decreasing the density of the balloon) will widen the difference in densities, and thus create more lift.$\endgroup$
– MozerShmozerNov 14 '16 at 16:47

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$\begingroup$@MozerShmozer I think you mean >>>>54 liters ("much much much greater than"), you'd need 54,687 liters of hard vacuum to lift a 70 kg person. Unless, that is, air on your planet weighs 1.28 kilograms rather than 1.28 grams, then you've got the correct value. The lifting force is the weight difference per volume of displaced air. So with vacuum (near-zero density gas), you need to displace a volume of air equal to the mass you want to lift just to become neutrally buoyant.$\endgroup$
– SamuelNov 14 '16 at 23:22

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$\begingroup$@Samuel Ah, yes. I accidentally recorded my volume as Litres, when it was actually in Cubic Metres. Good catch.$\endgroup$
– MozerShmozerNov 14 '16 at 23:36

4 Answers
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A fish has it easy, it can just take some of the gasses dissolved in the water and pump them into its bladder with enough pressure to stand the exterior pressure. Since gasses are way lighter than water, it does not need a very large bladder.

Now, you have your humbird (human bird) with his bladder. The first issue is that it must be HUGE. Since air only weights slightly over a kilogram per cubic meter, the most buoyancy you get will be that 1.225kg per cubic meter (at sea level, less as you rise), and that assumes that the bladder is void.

But let's forget about that and guess that you are happy with that "humzeppelin" design. Then appears the issue of how to fill that gigantic space.

If you leave it void you need a very strong structure to avoid it being crushed by atmospheric pressure (ever tried the experiment of making the void in a can?). Strong structures are heavy.

You may fill it with something to avoid or limit the pressure differential. But.. what? The gas that you have freely available is the same that the one you have to float on, so it is not going to provide much lift. Heating that gas might help, but then again you will need important amounts of fuel to heat such a gas, and it is not like you can ignite fires in the interior of living beings.

You may try to justify that your animal has some internal deposits of, say, compressed helium inside (again, compressing helium is not small feat for a living being), but the issue is again where will you get your helium from (free helium is light, so it goes to the upper atmosphere and goes into space; our supply of helium comes as byproducts of nuclear decay that got trapped in oil deposits).

Another option would be the animal producing hydrogen by some chemical reaction, that is feasible but is a great risk for the animal (not only because what happened to the "Hindenburg" but also because hydrogen is highly reactive with organic tissues).

Getting lift is the only problem. People are innately able to get to the ground from any height without external assistance. The ratios are well known.

A) It's possible, but not even close to feasible to "filter specific gasses" like hydrogen or helium from the atmosphere at ground level in order to lift a human (about 68 cubic meters for helium). It's more feasible to generate, from water via electrolysis, enough hydrogen to a lift a human (about 58 cubic meters).

B) One things to consider is that the difference between a human's density and their surrounding medium is significantly different than the difference between a fish's density and its surrounding medium. This means a fish can make rather subtle adjustments to change its vertical position, but a human needs to inflate a balloon the size of a shipping container. Additionally, while fish can swim at any height in the water, humans can't walk once they're four inches off the ground. Floating humans will just blow in the wind.

This idea was explored in Neal Stephenson's book Anathem. Humans in this book had spheres which increased their volume without allowing air or any other gasses to enter them. That is, they filled with vacuum. Which is an even better "lifting gas" than helium or hydrogen (marginally). If you're not restricted to hard science, I suggest you explore the vacuum lifting spheres, then there is no need to mess with filtering rare gasses out of the atmosphere.

Modern technology has no problems creating a device that floats thanks to LTA gas or is assisted by it. Evolution has created systems in animals that are even beyond our current level of technology, even very complex constructs have been found. I.E. the chameleon which uses nano-crystals to archive it's color change, something that could be very beneficial for modern displays once it is fully understood. There is no reason to believe that even a complex system to fly using LTA gas is impossible.

Evolution does create things "randomly", but if it turns out to be a disadvantage for the species it literally dies out, if it is an advantage, it will strife, if it is neither it might continue to exist in one form or another. So if LTA gas is something that is an essential part of a species, it has to provide some benefit to this species. There might also be species that have a 'left-over' version of LTA gas flight, that does not put them at a disadvantage, but doesn't necessarily provide any noticeably benefit either.

The amount of LTA gas required to cancel out gravity is enormous. Compare the size of the man in the picture to the volume of helium necessary to lift him up and consider that the amount of gas necessary to lift an even bigger species raised exponentially. Getting an animal the size of an elephant to fly with balloons would require so many, that the elephant would look tiny in comparison.

Any larger species that uses LTA gas as their main system of lift would have to look massively bloated. As friction raises with the surface area (drag), such a species would be either very slow, or it would have to have a body that would reduce friction. A flying squid would barely be able to fight the force caused by wind on his body, a flying Manta could however be very maneuverable. Water-based creatures serve as good examples here, as they have to fight the same issues at a smaller level.

Further issues caused by LTA gas like flammability, leaking, producing gas reserves are no relevant issue, because if such a species would exist, it would have already been solved in a clever manner, otherwise they would have died out at some point and it wouldn't exist. Gas sacks would be sufficiently covered by dense tissue to prevent leaks from predator attacks, and even rare gasses could be created by that species organism at a sufficient rate. There are bacteria that turn iron into gold, so why shouldn't there be an organism that somehow produces helium?

So why are there no LTA gas flying species around here?

The main reason would be that evolution favors simpler creatures, as they can adapt to environmental changes easier than complex creatures that require a very specific Eco-system to exist. Additionally mutations do not happen instantly to something completely random, but gradually, so there had to be a base creature with an air bladder that slowly evolved step by step into a flying creature with LTA gas, which may simply have never happened, or the creature died out on the way.

Huge flying creatures that would benefit from the lift of LTA gas bladders could have evolved, but such a species would require more food thanks to it's size, and therefore it would be more dependent on a vivid Eco-system to get that food. A simple drought could have killed such a species or it's ancestors before it became widely spread, similar to how dinosaurs died out from a sudden change to the Eco-system.

Summary

A species flying with the help or entirely based on LTA gas bladders is possible, but unlikely to evolve by natural cause on this planet, as it is complicated yet provides no substantial benefit over simpler alternatives. This could be entirely different in entirely different Eco-systems, or with magically accelerated evolution. So a creature flying thanks to gas bladders is entirely possible in a different world, but not necessary.

That's exactly what you're talking about - a hydrogen or helium balloon. Of course, it can't be nearly as compact as a fish's swim bladder because air is so much less dense than water. To get enough of a difference to lift a person, you need something the size of a balloon.

$\begingroup$Balloons come in lots of different sizes. How large would it need to be to lift a person if it were hydrogen, helium, or some other lifting gas?$\endgroup$
– MozerShmozerNov 11 '16 at 19:43

$\begingroup$Helium has a lifting force of about 1 gram per litres. Let's say the average person weighs around 70 kg, you'd need 70,000 litres of helium to lift him.$\endgroup$
– WerrfNov 11 '16 at 19:45

$\begingroup$Does a hydrogen or helium balloon regulate its contents to make minute adjustments to buoyancy? As far as I know, I did not just invent the balloon. There is much more to consider here.$\endgroup$
– ZxyrraNov 11 '16 at 23:16

$\begingroup$@Zxyrra making minute adjustments to bouyancy is meaningless if the device doesn't provide any bouyancy.$\endgroup$
– WerrfNov 12 '16 at 0:06